The ingredients of Kevin Guilfoile’s fast and furious new thriller will be familiar to many readers:

A haunted but ferocious sprite of a heroine who, like Lisbeth Salander in Stieg Larsson’s novels about the girl with the dragon tattoo, has a cyberquick mind and is on the run from malevolent enemies.

A mysterious organization, reminiscent of the Priory of Sion in Dan Brown’s “Da Vinci Code,” that guards startling historical secrets and sits at the center of a maze-like plot featuring lots of cryptic symbols.

A respected Chicago lawyer who, not unlike the hero of Scott Turow’s “Presumed Innocent” and “Innocent,” gets involved in a sensational case that may put him in legal jeopardy.

It’s hard to imagine that a novelist could lift such elements from several of the best-known bestsellers of recent years and turn them into something original and gripping, but that’s exactly what Guilfoile has done in “The Thousand.” Though there’s some ridiculous mumbo jumbo about the secret society and though some of the complicated plot points end up not making a whole lot of sense, the book is jet-fueled by its author’s unerring sense of character and nimble prose.

Just as he remade the Frankenstein myth in his first novel, 2005’s “Cast of Shadows,” (with a little inspiration from Michael Crichton and Robin Cook), so he manages to take a handful of well-trodden concepts here and shape them into a suspenseful read that’s all his own.

Guilfoile’s heroine, Canada Gold (or Nada, as she is known) is the girl with a digital brain. As a teenager suffering from acute attention-deficit hyperactivity disorder, she was subjected to an experimental procedure involving the implant of a neurostimulator in her head. As a result, she has a computer-like ability to harvest and process information, which gives her uncanny insights into people and an astonishing facility with numbers. This ability also facilitates her careers as a private investigator and a premier poker and blackjack player on the watch list at many Vegas casinos.

Nada’s father is Solomon Gold, an Oscar-winning composer and music director of the Chicago Symphony Orchestra. He had been charged with the murder of Erica Liu, a young cellist in the orchestra with whom he had been having an affair, but was acquitted, in large part because of the skills of his dashing lawyer, Reggie Vallentine, who would go on to gain fame, fortune and a bad conscience from his defense. Shortly after the trial, Gold was murdered, and Reggie was seriously wounded.

“The case had been closed the next day,” Guilfoile writes, “when Erica Liu’s father, Michael, the primary ‘person of interest,’ killed himself without leaving a note.”

We also learn that, on the night of his death, Gold told Reggie he had written a completion of Mozart’s Requiem in D minor — a project, he insists, based on a secret mathematical map that enabled him to re-create exactly what Mozart himself had in mind.

“There are people who won’t want me to publish this,” Gold ominously confided. “They’ll think it blasphemy. Dangerous even. If they knew my intentions to do so, they would do anything to stop me.”

Ten years later, the gun used to kill Solomon Gold turns up in another murder case — of Nada’s doctor, strangely enough — Marlena Falcone, who implanted the neurostimulator. With these developments, a nervous Reggie suddenly finds himself being questioned by a friend, detective Bobby Kloska, about the night Gold was killed.

Meanwhile, unknown persons — possibly connected with Falcone’s murder — are hot on the trail of Nada, who has left Las Vegas to undertake an assignment from a Chicago art collector named Jameson that draws upon her puzzle-solving gifts: She is to look into an eccentric artist’s mysterious masterwork, made up of thousands of individually painted tiles that may reveal an important message, or that may be just an elaborate hoax.

What connects these events, it turns out, is a sinister organization called the Thousand, made up of followers of Pythagoras, the mathematician and philosopher from ancient Greece.

As Guilfoile describes it, this organization is part Skull and Bones, part Masonic lodge, part something more twisted and nefarious: Its members are supposedly privy to certain mathematical secrets that they believe will destroy the world if revealed to the ignorant masses. The organization appears to be split into two camps that are at war with each other: mathematici, who want to use their knowledge to enrich themselves, and acusmatici, who want to keep their knowledge under wraps.

All this silliness is somehow made beguiling by Guilfoile, who has the sleight-of-hand skills and showmanship of a Vegas magician, juggling several intersecting plot lines, cutting back and forth among them to build tension and a sense of impending danger. The novel’s conclusion is disappointing (much the way the ending of “The Da Vinci Code” was disappointing), as many of the provocative questions raised by the author are left flapping in the wind.

But then, the real pleasures of reading “The Thousand” have less to do with the story’s portentously withheld secrets than with Guilfoile’s keenly observed characters, gritty feel for the city of Chicago and ability to weave all sorts of philosophical questions — like the relationship of music and math, and the morality of using scientific knowledge — into his hectic, bloodstained plot.

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